Conjugate Heat Transfer

We specialize in solving conjugate heat transfer (CHT) problems in solids, liquids, and gasses for diverse kinds of electromagnetic heating sources including resistive, inductive and microwave. It is still quite common to study electromagnetics independently from fluid dynamics, which reduces problem complexity but is less accurate compared to fully coupled multiphysics problems due to neglected temperature-dependent properties and losses.

Our approach is coupled, we use accurate models that are particularly suitable for designing smaller, lighter, energy-efficient and more reliable electrical devices with lower margins for error.

Passive cooling of PCB plate

Heat sink thermal resistance can be estimated from actual PCB flow patterns and from different air conditions, including inlet temperature and humidity.

Air Flow Through Electric Heater

This example shows a reduced model of the domestic heater where constant electric current is passing through the coils with temperature-dependent conductivity. The model consists of boundary conditions imitating air flow through the ventilator and high turbulence flow. Turbulence is important for heat removal from surfaces and it is many times more effective than laminar flow.

The electromagnetic part of the problem is solved by Elmer FEM using temperature-dependent material properties.


– Electrical conductivity
– Permeability for induction (Curie–Weiss law)
– Permittivity for microwaves

The practical applications of CHT models extend far beyond the design of heating equipment; other uses include designing transformers, electrical motors and flow sensors.

Transformers and chokes

Numerical simulations can help with the thermal management of transformers and chokes. The use of ferrites with nonhomogeneous, temperature-dependent permeabilities and high frequencies make analytic calculations challenging and inaccurate.

Liquid Cooling of Electrical Motor

Energy that is not turned into useful work, like turning the rotor, is wasted as heat that needs to be removed. Accumulation of heat leads to high temperatures that can decrease motor efficiency due to increased electrical resistance of the copper windings. In more serious cases overheating causes demagnetization of permanent magnets and dielectric material (Epoxy, Plastics) breakup.

Heat losses generated in fluids or solids are sent to CFD software OpenFOAM. There are models for various flow regimes (laminar, turbulent) and convection types (natural, forced). Temperature-dependent properties include


– Viscosity
– Density
– Phase-change
– Heat capacity
– Thermal conductivity

Efficient coupling between Elmer and OpenFOAM is enabled by our software EOF-Library.

It allows efficient internal field interpolation and communication between the finite element (FEM) and the finite volume frameworks (FVM). The simulation runs until steady-state or specified end time are reached.

SIA EOF Consulting ir noslēdzis 28.02.2020 līgumu Nr. VP-L-2020/12 ar Latvijas Investīciju un Attīstības Aģentūru par atbalsta saņemšanu vaučera programmas ietvaros. Pētījuma mērķis ir veikt eksperimentālo izstrādi, lai atrisinātu 3 industriālu problēmu modeļuzdevumus. EOF Consulting LLC signed contracts BIZIN-I-2019/731 and SKV-L-2019/115 with LIAA for recieving support from ERAF projects ( and

We received a grant from Olaine municipality as part of the Iedvesma competition: